Vozniak A. Investigation of uniform, pendulum and precessional gyrostat movements with variable gyrostatic moment

The thesis is devoted to the study of the conditions for the existence of uniform, pendulum and precessional gyrostat movements with a variable gyrostatic moment carrying one and two rotors, under the action of potential and gyroscopic forces. New solutions of the Kirchhoff-Poisson equations for the motion of a gyrostat under the action of potential and gyroscopic forces describing the uniform rotation of the gyrostat in two problems (the problem of the gyrostat motion with one rotor and the problem of gyrostat motion with two rotors) are obtained. Conditions for existence both of pendulum movements and the semi-regular precessions of a gyrostat carrying one rotor and two rotors, under the action of potential and gyroscopic forces, are found. These solutions are characterized by the fact that the angle of their own rotation is either an elementary function of time or an elliptic function of time. For the cases of spherical and axisymmetric mass distribution new solutions of the gyrostat movement equations, which describe the semi-regular precession of the gyrostat, are found.